Will an electron vibrating in a 1D radiates?

[thitchen]

Hi all,

According to quantum theory, for an electron vibrating in one dimension, only probability of position is meaningful. My question is will there be a e&m radiation by such a motion, if yes, how to appreciate it from the possibility argument, say, if only the probability at each position is the true description of such a motion, how come there comes up with a frequency of the motion.
If no, will there be a radiation by an oscillating ion in one dimension? I find it very difficult to go from classical to quantum picture, anyone please help. Thank you very much.

 

[tom.stoer]

I am not sure about the context.

In principle this is a problem which can be described classically using Maxwell's equations. Then it is possible to quantize the system in order to understand QED corrections.

Then I am not sure what you mean by "vibrating in one dimension". Does the electron live I am three dimensions but vibrates along a line? Or do you want to study the one-dimensional system, i.e. 1-dim. QED. In the latter case there is no radiation in the usual sense b/c up to one single QM d.o.f. the el.-mag. field is pure gauge.

 

[thitchen]

Hi Tom,

Wow, thank you so much for your reply. Yes, the context is the electron lives in 3D world but vibrates in 1 direction. Sorry for the confusion. I only learn undergrad QM,and I'm afraid I never touched QED before.

The exact problem is for a molecule adsorbed on top of a metal surface, more likely the charge in the molecule will be redistributed due to the adsorption. And meanwhile the molecule can vibrate/bounce up and down on the surface, will there be a radiation? And will the radiation be large enough to interact with an incoming tunneling electron fron a metal tip(STM), I mean is it worth to consider radiation in this context?

Thank you again for your reply, Tom, and thank you for pointing me the right direction, I think I need to struggle some more to get help from QED then.

-Chen

 

[ZapperZ]

I also don't understand this question, and why it is in the quantum physics forum.

A line antenna can easily be considered as electron "vibrating in 1D". This is classical E&M. Is this not the same as what you are asking?

Zz.

 

[thitchen]

Hi Zz,

I'm sorry I don't know this should not be posted here, I'm afraid, is there a way to repost/redirect it somewhere else?
The electron lives in 3D, but vibrates in 1direction.
I just find it difficult to appreciate that since if only the probability of position of electron is the true description. How come the electron is "vibrating", I mean, how to connect this two pictures together, one classical vibrator and one quantum description, sorry if the question is silly, but I really can't relate this two pictures.

 

[ZapperZ]

Hi Zz,

I'm sorry I don't know this should not be posted here, I'm afraid, is there a way to repost/redirect it somewhere else?
The electron lives in 3D, but vibrates in 1direction.
I just find it difficult to appreciate that since if only the probability of position of electron is the true description. How come the electron is "vibrating", I mean, how to connect this two pictures together, one classical vibrator and one quantum description, sorry if the question is silly, but I really can't relate this two pictures.

You never answered my question. Why is the 1D antenna that I mentioned different from what you are asking? I'm guessing that since you have done undergrad QM, you should also have done similar level E&M and would have seen the classical E&M problem of 1D antenna. So if you didn't have a problem with that, why are you having a problem here?

In principle, I can take a bunch of electrons, shake it up and down (i.e. in 1D), and voila! I've created EM radiation, just like the antenna. Isn't this what you want?

Zz.

 

[thitchen]

Hi Zz,

Thank you for your reply.

Yes, indeed, it can be described in classical language.

But it can also be described in the quantum language, say the probability at each position along x axis, correct?

My question is how to relate this two pictures together?

My understanding is that the pure description by probability does not necessarily lead to a periodic motion, correct?

You never answered my question. Why is the 1D antenna that I mentioned different from what you are asking? I'm guessing that since you have done undergrad QM, you should also have done similar level E&M and would have seen the classical E&M problem of 1D antenna. So if you didn't have a problem with that, why are you having a problem here?

In principle, I can take a bunch of electrons, shake it up and down (i.e. in 1D), and voila! I've created EM radiation, just like the antenna. Isn't this what you want?

Zz.

 

[Jano L.]

My understanding is that the pure description by probability does not necessarily lead to a periodic motion, correct?

Yes, that is right. But quantum theory or Schr. equation is not purely probability theory. Periodic oscillations of charge can arise, for example when the wave function is superposition of two eigenfunctions of the Hamiltonian, or when the model refers to an atom in the field of external periodic wave.